How to calculate correlation coefficients for each corresponding pixel of two images(of same dimensions)? I need the output also to be of same dimension.

I am trying to implement a paper titled "Detection of microaneurysms using multi-scale correlation coefficients ".

https://www.sciencedirect.com/science/article/pii/S003132031000004X

In that, we are supposed to extract green channel image from rgb retinal image [ fig 7(a) ] and apply a gaussian filter with five different sigma values(1.1,1.2,1.3,1.4,1.5) to the green chanel image to get 5 corresponding gaussian blur images.Now,we have one original image and 5 gaussian blur images.

Now,Correlation coeffient of the green channel image and each of the five blur images is calculated pixel wise to get five corresponding matrices.

The maximum response for each corresponding pixel in the five output matrices values will be selected and a new matrix is formed with them.This new matrix is the final output matrix [ fig7(b) ].

i have tried using all correlation functions like corr2,corrcoeff but of no use since i want an output matrix of same dimensions as input images.

The input and output should look like this:

Can someone give any insights on how to compute correlation coeffients for each pixel to get the required output?

This is the first step mentioned in paper: "The first step in coarse level candidate detection involves applying a sliding neighborhood filter with multi-scale Gaussian kernels to the fundus image in order to calculate a correlation coefficient for each pixel."

Thank you.

Answer 1

[Thiago Henrique Gomes Lobato]

I believe they used a slided window cross correlation, which is basically the same as if you use corr2 (which will give you just one value) in all possible overlaping combinations of the two images, which would force you to pad one of them, so the dimensions would always be right. This is basically the same as the function normxcorr2 does. So you can use it in the two images and then remove the added pad, so you end up with same dimensions. Here's an example for a random image, where the auto correlation coefficient is expected to be 1 when the images exactly meet (at the center) and close to 0 elsewhere:

A = randn(7);
C = normxcorr2 (A,A);
ExtraPad = (length(A)-1)/2+1;
C = C(ExtraPad:end-ExtraPad+1,ExtraPad:end-ExtraPad+1);
figure,imagesc(C)

[Krishna Chaitanya]

Thanks for the reply. I tried implementing your suggestion but i didn't get the desired output as in fig 7(b) above.Can you please suggest any other alternative approach.

[Thiago Henrique Gomes Lobato]

There may be something else in your code. Could you post it here together with the image you used?

[Krishna Chaitanya]

i am enclosing the images which i have used 'sample.jpg' is the original rgb image in fig 7(a) above, 'green_sample.jpg' is the green channel version of the 'sample.jpg' and 'blur_img.jpg' is the output of gaussian blur on 'green_sample.jpg'.output.jpg is the final correlation output i.e, C.

the dimensions of input image are not equal.

Here is the code i used:

rgbImage = imread('sample.jpg');
greenChannel = rgbImage(:,:,2);
imwrite(greenChannel,'green_sample.jpg');
green_img = imread('green_sample.jpg');
gauss_kernel = fspecial("gaussian",5, 1.1);
blur_img = imfilter(green_img,gauss_kernel,"same");
C = normxcorr2(green_img,blur_img);
ExtraPad = (length(green_img)-1)/2+1;
C = C(ExtraPad:end-ExtraPad+1,ExtraPad:end-ExtraPad+1);
figure,imagesc(C)
imwrite(C,'output.jpg');

[Thiago Henrique Gomes Lobato]

Okay, I just quickly read the paper section after seeing your code and the problem is just a interpretation matter. They don't take the correlation of the original image with the blurred one, but rather of the image with the Gaussian kernel. The idea is that microaneurysms look like Gaussian distributions and thus should have a good correlation with them and, since they may have different sizes, the use of multiple scaled Gaussian kernels may account for that difference if one uses the maximum coefficient between all. A version that does what you actually want looks like this:

rgbImage = imread('sample.jpg');
greenChannel = rgbImage(:,:,2);

AllKernelsSTD = [1.1,1.2,1.3,1.4,1.5];
WindowsSize = [13,15,17,19,21]; % Approximate values based in the kernel image in the paper
C = zeros(size(greenChannel,1),size(greenChannel,2),length(AllKernelsSTD));
for idxK=1:1
gauss_kernel = fspecial("gaussian",WindowsSize(idxK), AllKernelsSTD(idxK));
Ctemp        = abs(normxcorr2(gauss_kernel,green_img)); % They consider just the magnitude of the correlation
ExtraPad = (length(gauss_kernel)-1)/2+1;
C(:,:,idxK) = Ctemp(ExtraPad:end-ExtraPad+1,ExtraPad:end-ExtraPad+1);
end
Cmax = max(C,[],3); % Maximum correlations between all Kernels
figure,imagesc(Cmax),caxis([0.2,1]),colormap('gray')

Since they are not very exact about the kernel sizes, you could tweak with it a little for closer results, and depending of how you got the image (if you just printed or have the actual used file), different image scales/sizes may demand the use of accordingly kernel sizes.

[Krishna Chaitanya]

Thank you very much!

[Krishna Chaitanya]

Hello Thiago,i can observe the noise outside the retinal image(i.e, the white spots outside the circle of the retina)at the edges of the image.Can you help me in removing that noise?

Thank you

[Thiago Henrique Gomes Lobato]

Hi Krishna, it depends what exactly you mean by removing. For example, if you set a treshold in the image for all values below a tol to be 0 and perform some filtering as a median filter they will probably be totally removed, however together with some noise inside the retinal image (this approach would be also the easier one). If you want to remove everything outside the retina without changing anything in the internal part , you need first to find all points outside it and set them to 0, you can either do it manually of with some heuristic, like setting a radius from the center of the image which would correspond to the retina and than setting every pixel outside this radius to zero.

[Krishna Chaitanya]

I want every pixel out of the boundary of circle to be set to zero (as you said in the second case in your above comment).Can you please provide me some code for that task .

Thank you